During the last decades a consensus has emerged that it is impossible to disentangle liquidity shocks from solvency shocks. As a consequence the classical lender of last resort rules, as defined by Thornton and Bagehot, based on lending to solvent illiquid institutions appear ill-suited to this environment. We summarize here the main contributions that have developed considering this new paradigm and discuss how institutional features relating to bank closure policy influences lender of last resort and other safety net issues. We devote particular emphasis to the analysis of systemic risk and contagion in banking and the role of the lender of last resort to prevent it.